Problem: What is the value of the following logarithm? $\log_{64} 8$
Solution: If $b^y = x$ , then $\log_{b} x = y$ Notice that $8$ is the square root of $64$ That is, $\sqrt{64} = 64^{1/2} = 8$ Thus, $\log_{64} 8 = \dfrac{1}{2}$.